Disadvantaged pupils are those pupils whose ability to learn in school is impeded by their family, social or economic situations which are often times beyond their control. Without adequate intervention, there are chances that this group of pupils could drop out of school. In Nigeria, there are many categories of disadvantaged pupils into which a vast majority of pupils can be grouped. Providing science education requires a lot of resources and organization. By its nature, the engagement of children in science education under an ideal environment is a huge task, let alone for pupils who are disadvantaged and must learn science under abnormal circumstances. The gravity of the disadvantage suffered by these pupils vary, hence, this paper focuses on two very critical groups of disadvantaged pupils in Nigeria (the pastoralist nomads and the Almajiris) and describes the challenges faced by educators in providing science education to them. The paper further presents a critical appraisal of some national and international educational programs which are designed to assist educationally disadvantaged pupils with an intention to explore the successes and failures of such programs within the Nigerian context. Some recommendations on how to tackle the identified challenges are proposed.